A method for controlling a wind turbine power system connected to an electrical grid includes determining, via a controller, at least one non-linear magnetizing parameter of a double-fed wind turbine generator of the wind turbine power system. The method also includes developing, via the controller, a model of the non-linear magnetizing parameter(s) of the double-fed wind turbine generator. Further, the method includes using, via the controller, the model in a stator voltage regulator of the double-fed wind turbine generator to provide grid-forming control of the double-fed wind turbine generator.